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4 years ago ::
Jul 15, 2009 - 3:27PM
#1
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Date Joined:
Jan 23, 2008
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High Imaskar FRPG background states
[INDENT]you can reroll any Arcana check, but you must keep the second result, even if it is worse[/INDENT]
Arcane Insight (Wizard utility 2 encounter power)
[INDENT]Free action
Trigger: you make an arcana check and dislike the result
Effect: Roll an Additional Arcana check, keeping the better of the two results.[/INDENT]
Let's say you want to make an arcana check. You roll for the first time and use the high imaskar to reroll it, yet dislike it, triggering arcane insight. You roll an additional arcana check, which High imaskar lets you reroll keeping the second. Imaskar states that you must keep the second, and I am keeping the second roll for that arcana check. Insight lets me choose between the 2 results. Arcane insight says you keep the better of the results.
roll 1
(optional) want to reroll, so reroll(1b) keeping the second
dislike the result
use Arcane insight
roll 2
(optional) want to reroll, so reroll(2b) keeping the second
if neither rolls used high Imaskar then arcane insight uses max(roll 1,roll 2)
if you used Imaskar on first roll then max(roll 1b,roll 2)
if you used Imaskar on both rolls then max(roll 1b,roll 2b)
if you used Imaskar on latter roll then max(roll 1,roll 2b)
Do I have this right?
Later I'll do the probability of achieving a certain results
DPR King Candidates 3.0How much damage should I shoot for?
Show
You're fired : 1 Kills Per 5 Rounds = .2 KPR
Fair Striker : 2 Kills Per 5 Rounds = .4 KPR
Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR
Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR
It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
Show
DPR = Damage Per round ~= Chance to hit * damage on a hit
KPR = Kills Per Round. 1 Kill = 8*Level+24 damage
= DPR/(8*level+24)
KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
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4 years ago ::
Jul 15, 2009 - 3:46PM
#2
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Date Joined:
Jan 23, 2008
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If you can do as I outlined I have done a programming test and these are the results:
Arcana check difference goal(DC - bonus) - probability of getting it
2 99.999
3 99.988
4 99.951
5 99.839
6 99.573
7 99.148
8 98.499
9 97.343
10 95.852
11 93.78
12 90.793
13 87.17
14 82.114
15 75.981
16 68.088
17 59.166
18 47.763
19 34.309
20 18.644
DPR King Candidates 3.0How much damage should I shoot for?
Show
You're fired : 1 Kills Per 5 Rounds = .2 KPR
Fair Striker : 2 Kills Per 5 Rounds = .4 KPR
Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR
Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR
It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
Show
DPR = Damage Per round ~= Chance to hit * damage on a hit
KPR = Kills Per Round. 1 Kill = 8*Level+24 damage
= DPR/(8*level+24)
KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
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4 years ago ::
Jul 15, 2009 - 4:01PM
#3
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This, like many things in 4.0, is an arguement more or less about semantics. Lets look at the two abilities you are using: you can reroll any Arcana check, but you must keep the second result, even if it is worse
Free action
Trigger: you make an arcana check and dislike the result
Effect: Roll an AdditionalArcana check, keeping the better of the two results.
Bolded text added for emphasis. The first ability allows you to reroll an arcane check die, so despite having two rolls, you only have one "die" on the table. This is different from rolling an additional die, because now you are making two seperate checks and simply taking the higher of each one. Because each of these is a seperate arcana roll, your backround property would apply to both, as they are both individual arcana rolls. Here's the rundown:
1) Roll an arcana check (1d20+??). Hypothetical result of 10.
This triggers backround ability to reroll if you so choose.
1b) Rerolling arcana check #1 (1d20+??). Hypothetical result of 14. (note that any conditional modifiers to your first roll also affect your reroll)
Your arcana check is 14.
At this time, you may use you Wizard Utility to gain another arcana roll
2) Roll an arcana check (1d20+??). Hypothetical result of 9.
Since it's its own arcana check, you can use your backround power to reroll this if you choose.
2b) Reroll your check (1d20+??). Hypothetical result of 24. (note that any conditional modifiers to your first roll also affect your reroll).
Take the highest of your two results (14 and 24) and your roll is 24.
[s]1) 10
Reroll: 1b) 14
[s]2) 9
Reroll: 24
14<24=result of 24.
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4 years ago ::
Jul 16, 2009 - 1:41PM
#4
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Date Joined:
Jan 23, 2008
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Here's some numbers I ran under the assumption that you get 2 rolls, take the better, and on each you can reroll forcing to take the second, as described above. I wanted to know the expected value, but that's difficult when you don't have a rule for when to reroll. Using arcane insight is obvious because you get to choose betwene the 2 rolls. But rolling once and deciding to take a gamble is difficult if you don't know when to take that gamble. I decided that I would set a goal, like for trying to achieve a set goal, and deciding to reroll if that goal isn't reached. Rolling twice and taking better for arcane insight, but for each of those rolls, if they are below the threshold reroll. In other words: I want a high Arcane check but am not told the set DC. I set my arbitrary goal to X (to be defined later) and roll 2d20. If the first is below my set goal there is no harm in rerolling it because I didn't meet my goal. I reroll my first. Let's assume it makes my goal, and my other die is good, but not as good as my first's reroll. Since I'll be taking my first rerolled die, if I reroll the second and it gets worse, thus there's no harm in rerolling the second die. I reroll if it does not meet my goal or is less than my first or first reroll. I performed this 100000 times for a goal from 2 to 20, and recorded the result and found the probability of getting a result X with a goal of Y. To find the expected value I did sum(x*y) and found which goal produced the greatest expected value. Goal Expected 2 14.78 3 14.94 4 15.14 5 15.29 6 15.43 7 15.59 8 15.68 9 15.79 10 15.88 11 15.97 12 16.02 13 16.04 14 15.99 15 15.93 16 15.78 17 15.57 18 15.28 19 14.91 20 14.44 The thing I took from this (If you plot it in excel) is that the prime number to set as an arbitrary goal is anywhere between 11-15 with significantly bad returns if you set your arbitrary goal above 17. here's my code Spoiler:
Show
Random rnd = new Random();
float[][] matrix = new float[19][];
for (int goal = 2; goal <= 20; goal++)
{
int n = 100000;
matrix[goal - 2] = new float[20];
for (int i = 0; i < n; i++)
{
int roll1 = rnd.Next(1, 21);
if(roll1 < goal) roll1 = rnd.Next(1,21);
int roll2 = rnd.Next(1, 21);
if (roll2 < goal || roll2 < roll1) roll2 = rnd.Next(1, 21);
int best = Math.Max(roll1, roll2);
matrix[goal - 2][best-1] += 1.0f / n;
}
Console.WriteLine("Goal = " + goal);
for (int i = 1; i <= 20; i++)
{
Console.WriteLine(matrix[goal - 2][i - 1]);
}
}
DPR King Candidates 3.0How much damage should I shoot for?
Show
You're fired : 1 Kills Per 5 Rounds = .2 KPR
Fair Striker : 2 Kills Per 5 Rounds = .4 KPR
Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR
Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR
It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
Show
DPR = Damage Per round ~= Chance to hit * damage on a hit
KPR = Kills Per Round. 1 Kill = 8*Level+24 damage
= DPR/(8*level+24)
KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
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4 years ago ::
Jul 16, 2009 - 11:33PM
#5
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You've inspired me to crunch some numbers. Suppose you want to maximize the expected value (not necessarily what one wants in a threshold system like d20 rolls, but it's what we'll assume). In that case, you should reroll the first check if it's less than 13, and reroll the second check if it's less than the first check or less than 11. This will get you an expected value of 16.044.
Edit: My bad, wasn't clever enough. You can get an expected value of 16.058 as follows (and this should be optimal):
Reroll the first check if it's less than 13. Reroll the second check if it's less than M + (20-M)*(21-M)/40, where M is the result of the first check.
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4 years ago ::
Jul 17, 2009 - 7:08AM
#6
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Date Joined:
Aug 22, 2005
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So, uh, can someone tell me what's the point of all this?  As in, why do we need/want 4 rerolls of Arcana?
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4 years ago ::
Jul 17, 2009 - 7:20AM
#7
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Date Joined:
Jan 23, 2008
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Sorry. Sage of ages's[AP] 24th level utility power gives you encounter long bonuses based on an arcana check. The Sage of the Ages lvl 24 ability is good enough as it is, but we also want to get +2 to attack and +2 to all defenses from Trick of Knowledge. For this, we need to make sure we make a DC 51 arcana check.
arcana check: 15(lvl)+9(int)+5(prof)+6(ed)+6(item)+2(r ace)+2(backgound)+2(Academy Master) -> 47 vs DC 51
Extra rolls: 1 from Arcane Insight, 1 from Keeper's Prescience -> roll 3x, use best
31-35: +5 saveing throws
36-40: +2 to all defenses
41-45: +2 arcane attacks
46-50: make saves at beginning of your turn
DC 51: 99.6625% (choose both the +2 to arcane attacks and +2 to all defenses)
DC 56: 93.6% % choose an additional option of: +5 to saves
DC 61: 72.5375% % choose an additional option of: make saves at the beginning of your turn instead of end
This is a quote from SongNSilence's FeyCharger build where he tries to get the +2 to attacks AND the +2 defences, using only the wizard's utility power Arcane insight. If we combine the background and the power our expected number goes up and thus the probability of getting more boosts.
There's a thread dedicated to getting a pure +50 to your arcana check, but I feel getting a 95% chance of doing so, while expending much less resources, is much better.
Also imagine you want to do a really good ritual based on arcana. Getting a sky high arcana check is awesome, and sometimes profitable.
DPR King Candidates 3.0How much damage should I shoot for?
Show
You're fired : 1 Kills Per 5 Rounds = .2 KPR
Fair Striker : 2 Kills Per 5 Rounds = .4 KPR
Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR
Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR
It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
Show
DPR = Damage Per round ~= Chance to hit * damage on a hit
KPR = Kills Per Round. 1 Kill = 8*Level+24 damage
= DPR/(8*level+24)
KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
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4 years ago ::
Jul 17, 2009 - 7:46AM
#8
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Decent approach for a Sage build, although I don't think I'd want to actually take the utility before 26th. So hard to give up Shield. 
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4 years ago ::
Jul 17, 2009 - 7:54AM
#9
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Date Joined:
Jan 23, 2008
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Fool's gold is arcana based and could prove profitable.
Really being able to max on most arcana based rituals is a handy thing. Going from an expected value of 10.5 to 16 (a +5.5) is worth quite a bit.
But shield is very nice.
DPR King Candidates 3.0How much damage should I shoot for?
Show
You're fired : 1 Kills Per 5 Rounds = .2 KPR
Fair Striker : 2 Kills Per 5 Rounds = .4 KPR
Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR
Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR
It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
Show
DPR = Damage Per round ~= Chance to hit * damage on a hit
KPR = Kills Per Round. 1 Kill = 8*Level+24 damage
= DPR/(8*level+24)
KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
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